Question: Express your answer as a mixed number simplified to lowest terms. $12\dfrac{1}{5}-4\dfrac{2}{7} = {?}$
Answer: Find a common denominator for the fractions: $= {12\dfrac{7}{35}}-{4\dfrac{10}{35}}$ Convert ${12\dfrac{7}{35}}$ to ${11 + \dfrac{35}{35} + \dfrac{7}{35}}$ So the problem becomes: ${11\dfrac{42}{35}}-{4\dfrac{10}{35}}$ Separate the whole numbers from the fractional parts: $= {11} + {\dfrac{42}{35}} - {4} - {\dfrac{10}{35}}$ Bring the whole numbers together and the fractions together: $= {11} - {4} + {\dfrac{42}{35}} - {\dfrac{10}{35}}$ Subtract the whole numbers: $=7 + {\dfrac{42}{35}} - {\dfrac{10}{35}}$ Subtract the fractions: $= 7+\dfrac{32}{35}$ Combine the whole and fractional parts into a mixed number: $= 7\dfrac{32}{35}$